Determination of the effective dielectric constant from the accurate solution of the Poisson equation

Constant dielectric (CD) and distance-dependent dielectric (DDD) functions are the most popular and widespread in the Molecular Mechanics simulations of large molecular systems. In this article, we present a simple procedure to derive an effective dielectric constant, epsilon (out,eff), for these two methods based on numerical solutions of the Poisson equation. It was found that because of the very approximate nature of the CD and DDD models there is no universal epsilon (out,eff), which will work equally well for all molecular systems. For example, different MD trajectories of the same molecule can produce different optimal epsilon (out,eff)s. The DDD function was found to yield better agreement with the numerical solutions of the Poisson equation than a CD model does. The reason is that a DDD function gives a better description of the electrostatic interactions at short distances between the atoms. Another interesting finding of this study is that under certain conditions epsilon (out,eff) can take negative values for a system of two atoms at a limited distance range. However, in principle, there is nothing to prevent the epsilon (out,eff) from taking negative values for specific conformations of some molecules.